增长指数的连续红移参数化
Contiguous redshift parameterizations of the growth index
摘要：
物质扰动的增长率可以用来区分不同的引力理论，并在宇宙学尺度上区分暗能量和修正引力，作为对观测到的宇宙加速的解释。我们建议在这里参数化的增长指数的函数的红移。第一个由$γ(a)=\tildeγ(a) \frac{1}{1+(a_{_{ttc}}/a)}+γ_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$给出，它在低/中红移参数化$\tildeγ(a)=γ_{_{late}}(a)= γ_0 + (1-a) γ_a$和高红移$γ_{_{early}}$常数值之间插值。例如，当将CMB包括到其余数据中时，可以使用我们的插值形式$γ(a)$，而在其他情况下可以使用形式$γ_{_{late}}(a)$。结果发现，提出的参数化实现了一个适合，是优于0.004%的增长率在$Λ$ CDM模型，优于0.014%的五重冷暗物质（QCDM）模型，并优于0.04%的单位Dvali-Gabadadze-Porrati（DGP）模型（与$Ω_m^0=0.27$）的整个红移范围高达$z_{_{CMB}}$。我们发现，增长指数参数$(γ_0,γ_a)$采取不同的值暗能量模型和修改的重力模型，例如$(0.5655,-0.02718)$的$Λ$ CDM模型和$(0.6418,0.06261)$的平坦DGP模型。这为未来的观测数据提供了一种区分模型的手段。
英文摘要：
The growth rate of matter perturbations can be used to distinguish between different gravity theories and to distinguish between dark energy and modified gravity at cosmological scales as an explanation to the observed cosmic acceleration. We suggest here parameterizations of the growth index as functions of the redshift. The first one is given by $γ(a)=\tildeγ(a) \frac{1}{1+(a_{_{ttc}}/a)}+γ_{_{early}} \frac{1}{1+(a/a_{_{ttc}})}$ that interpolates between a low/intermediate redshift parameterization $\tildeγ(a)=γ_{_{late}}(a)= γ_0 + (1-a) γ_a$ and a high redshift $γ_{_{early}}$ constant value. For example, our interpolated form $γ(a)$ can be used when including the CMB to the rest of the data while the form $γ_{_{late}}(a)$ can be used otherwise. It is found that the parameterizations proposed achieve a fit that is better than 0.004% for the growth rate in a $Λ$CDM model, better than 0.014% for Quintessence-Cold-Dark-Matter (QCDM) models, and better than 0.04% for the flat Dvali-Gabadadze-Porrati (DGP) model (with $Ω_m^0=0.27$) for the entire redshift range up to $z_{_{CMB}}$. We find that the growth index parameters $(γ_0,γ_a)$ take distinctive values for dark energy models and modified gravity models, e.g. $(0.5655,-0.02718)$ for the $Λ$CDM model and $(0.6418,0.06261)$ for the flat DGP model. This provides a means for future observational data to distinguish between the models.
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